Voro++

radical.cc – The radical Voronoi tessellation

This example script demonstrates the ability of the code to handle polydisperse packings using the Voronoi radical tessellation. The code makes use of two sample particle packings in a cube of side length 6: “pack_six_cube” contains 216 monodisperse particles of diameter 1, and “pack_six_cube_poly” contains 159 polydisperse particles with diameters ranging from 0.5 to 1.5. These packings were generated from a DEM pouring simulation using LAMMPS.

On lines 26 to 31, the code creates a container class, and uses it to compute a normal Voronoi tessellation for the monodisperse packing, that is shown on the left above – this section of the code is essentially identical to the previous import.cc demonstration.

On lines 37 to 42, the code makes use of the container_poly to compute the radical Voronoi tessellation. This class is a variant of the container class, that has the same functionality, except that a radius is stored for each particle. The import() routine requires an additional radius entry, so that the lines in “pack_six_cube_poly” have the form:

The radical Voronoi tessellation is shown on the right above. The weighting introduced by the radical tessellation ensures that each particle is exactly within its Voronoi cell.

Code listing

 1: // Radical Voronoi tessellation example code
 2: //
 3: // Author   : Chris H. Rycroft (LBL / UC Berkeley)
 4: // Email    : chr@alum.mit.edu
 5: // Date     : August 30th 2011
 6: 
 7: #include "voro++.hh"
 8: using namespace voro;
 9: 
10: // Set up constants for the container geometry
11: const double x_min=-3,x_max=3;
12: const double y_min=-3,y_max=3;
13: const double z_min=0,z_max=6;
14: 
15: // Set up the number of blocks that the container is divided
16: // into.
17: const int n_x=3,n_y=3,n_z=3;
18: 
19: int main() {
20: 
21:         // Create a container with the geometry given above, and make it
22:         // non-periodic in each of the three coordinates. Allocate space for
23:         // eight particles within each computational block. Import
24:         // the monodisperse test packing and output the Voronoi
25:         // tessellation in gnuplot and POV-Ray formats.
26:         container con(x_min,x_max,y_min,y_max,z_min,z_max,n_x,n_y,n_z,
27:                         false,false,false,8);
28:         con.import("pack_six_cube");
29:         con.draw_cells_gnuplot("pack_six_cube.gnu");
30:         con.draw_cells_pov("pack_six_cube_v.pov");
31:         con.draw_particles_pov("pack_six_cube_p.pov");
32: 
33:         // Create a container for polydisperse particles using the same
34:         // geometry as above. Import the polydisperse test packing and
35:         // output the Voronoi radical tessellation in gnuplot and POV-Ray
36:         // formats.
37:         container_poly conp(x_min,x_max,y_min,y_max,z_min,z_max,n_x,n_y,n_z,
38:                         false,false,false,8);
39:         conp.import("pack_six_cube_poly");
40:         conp.draw_cells_gnuplot("pack_six_cube_poly.gnu");
41:         conp.draw_cells_pov("pack_six_cube_poly_v.pov");
42:         conp.draw_particles_pov("pack_six_cube_poly_p.pov");
43: }